Question

Given the equation 4x2 − 8x 20 = 0, what are the values of h and k when the equation is written in vertex form a(x − h)2 k = 0?

Answer 1

The vertex form of the given quadratic equation is

$4(x-1)^{2} + 16 =0$.

According to the given question.

We have a quadratic equation

$4x^{2} -8x + 20 = 0$

Since, for the standard quadratic form is $ax^{2} +bx + c = y$, the vertex form of a quadratic equation is $y = a(x -h)^{2} + k$ where (h, k) is the vertex.    

And h and k can be calculated as

h = -b/2a and y = k

So, for the given equation $4x^{2} -8x + 20 =0$ the vertex (h, k) is given by

h = -(-8)/2(4) = 8/8 = 1   (X coordinate of vertex)

and,

$y =4x^{2} -8x+ 20$

substitute x = 1 in the above equation for the value of k

Y = 4(1)(1) - 8(1) + 20

⇒ Y = 4 - 8 + 20

⇒ Y = -4 + 20

⇒ Y = 16

so, k = 16          (Y coordinate of vertex)

Now, substitute the value of a, k and h in $y = a(x-h)^{2} + k$.

⇒  $0 =4(x-1)^{2} + 16$

Therefore, the vertex form of the given quadratic equation is

$4(x-1)^{2} + 16 =0$.

Find out more information about vertex form of a quadratic equation here:

brainly.com/question/12223454

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